Please help me: If cos^4 3 x - sin^4 3 x = cos (g(x)), then
g(x) = .
use a^4-b^4=(a^2-b^2)(a^2+b^2)!

Question

Please help me: If cos^4 3 x - sin^4 3 x = cos (g(x)), then 
g(x) = . 
use a^4-b^4=(a^2-b^2)(a^2+b^2)!

zepdrix · Answer

Using the Identity that they provided gives us this,$$\large \cos^43x-\sin^43x=(\cos^23x-\sin^23x)(\cos^23x+\sin^23x)$$

Using information from part A, you should be able to simplify the `first` set of brackets.

To simplify the second set of brackets, revisit this formula, one of the first trig identities that they teach you.

$$\large \cos^2\theta+\sin^2\theta=1$$